Ideal Gas Law SIM [PDF]

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IDEAL GAS LAW SIMULATION Introduction This experiment explores the relation between the quantity of pressure P, volume V, and temperature T of an ideal gas of N number of particles. The ideal gas law is given by,

PV = n R T Where n is number of moles = N/(Avogadro number) and R is the gas constant. It can also be shown that

nR=Nk B where k B = 1.38 x 10 -23 J/K is the Boltzmann constant. Submit your answers using Blackboard.

1 – Exploring the Relations Between P,V,N,T Open the following simulation and select Explore (https://phet.colorado.edu/sims/html/gas-properties/latest/gas-properties_en.html )

Use the pump to add some particles. 1. For a fixed N and V, which quantity will increase the pressure if you increase it? 2. For a fixed N and T, which quantity will increase the pressure if you decrease it? 3. For a fixed V and T, which quantity will increase the pressure if you decrease it? Display the ‘Collision Counter’ and click on the green play button to start it. 4. If you increase only T does the number of collisions increase? (you have to start the counting again) 5. If you decrease only V does the number of collisions decrease?

Add some red particles to obtain a mix of blue and red particles. 6. Do the red particles move at the same speed as the blue particles? 7. Are the red particles more massive than the blue particles? Restart the simulation and decrease the volume to its minimal possible value (use the mouse to drag the handle located on the left of the container). By clicking on Particles, set N = 400 of the blue particles and N = 0 red particles. Check the value of the temperature: it should be 300K, if not start over and repeat. 8. Use the Ideal Gas Law to calculate the minimum volume.

2 – Ideal Gas Law Using the same simulation select Ideal. Use the pump to add some particles. Select Hold Constant Volume. 9. What happens to P if you increase T? 10. What happens to P if you increase N? Start over and click on Particles and add 100 heavy (blue) particles. Set the pressure to be constant with variable volume ↕V. Temperature at 300 K. Note the initial volume Vi. Now add 50 more blue particles so that the volume is now Vf. 11. What happens to the volume? 12. By using the ideal gas law, what is the ratio of Vf / Vi ? Next you want to find the work done by the gas as the number of particles changed from 100 to 150 while P and T stay constant. You can display the horizontal width by clicking on ‘Width’ 13. Which formula gives the work done by a gas when the volume changes at constant pressure? Assume the cross sectional area (into the page) is A = 60 x 10-18 m2. 14. Calculate the work done by the gas.

3 – Kinetic Theory Using the same simulation select Energy. Select Injection Temperature at 300 K, add some particles until the pressure in about 20 atm. C lick to display the Kinetic Energy (KE) as well. By looking at the plots 15. The number of particles with low speed is__than the number of particles with high speed. 16. The number of particles with low KE is __ than the number of particles with high KE. 17. If you add more particles to double the pressure, does the average speed increase? (no) 18. If you increase the temperature what happens to the average speed?

4 – The PV diagram Open this simulation (http://physics.bu.edu/~duffy/HTML5/PV_diagram.html)

Start by setting the volume = 6 L and Temperature = 600 K. 19. As you decrease the volume how does the pressure change? 20. As you decrease the temperature how does the pressure change? 21. As you increase the temperature how does the speed of the gas molecules change? 22. What is the value of the product nR for in this simulation? Set the temperature to 400 K. 23. For which value of the volume is the pressure 100 kPa? 24. For which value of the volume is the pressure 300 kPa? Use the ideal gas law to calculate the precise value and use the simulation to verify your answer.

5 – Find the number of moles. A physicist performs an experiment to evaluate the number of moles of a gas inside a container. The container is kept at constant room temperature of 23 °C and is built in such a way that the number of moles stays constant. The physicist changes the volume to different values and measures the corresponding (absolute) pressures. The table below shows the results of the experiment. V

50 ml

45 ml

40 ml

35 ml

30 ml

25 ml

P

168 kPa

194 kPa

215 kPa

248 kPa

287 kPa

377 kPa

Make a plot of P vs 1/V (if you plot P vs V the plot is not linear) and calculate the slope of the line. 25. Value of the slope = Assuming the gas obeys the ideal gas law, use the value of the slope to find the number of moles. Pay attention to using the correct units for all the quantities. For example the gas constant R has the value 8.314 if V is expressed in m 3 , P in Pascal and T in degrees Kelvin. 26. Number of moles n =